Worried that Mephisto might use the momentum to grow stronger one day?
You're overthinking it.
Lake had signed the contract under Saga's name, but his soul was still Lake's. The name and the soul didn't match, so this so-called contract was nothing more than a blank piece of paper.
Or rather...
The contract was only meant to bind Mephisto unilaterally. It didn't bind Lake.
Alliances with Mephisto hadn't been among Lake's original options. He had only chosen it because the timing happened to work out. Since he was going to fight a battle anyway, Lake had originally intended to make it a battle for prestige.
Simply put, Lake didn't care about the rewards from this battle. He only cared about the gains and losses in reputation.
But now?
There was loot to be had. Moreover, he could kill three birds with one stone. And since Mephisto had served up such an opportunity, it was better to drag Mephisto along than push him over to the other side.
After all, if he didn't make this deal, he would still need to help that Jane Foster evade the pursuit of Heaven's Fifth Legion so that the plan could proceed smoothly.
If he didn't involve Mephisto, Lake would essentially be working for Old Mo for free. That clearly didn't fit Lake's style. Since that was the case, why not make use of him?
The most important point was this.
If Mephisto joined in, he could serve as a smokescreen up front. Besides, Mephisto was an expert on Hell. Rather than taking over while completely in the dark, it was better to let Mephisto take charge first. Once Mephisto had sorted everything out, Lake could reclaim the ultimate authority.
That slut, Hell origin, was difficult to fool. Lake didn't want to deal with her